In a radioactive material, fraction of active material remaining after time $t$ is $\frac{9}{16}$ The fraction that was remaining after $\frac{t}{2}$ is 

Two radioactive materials $A$ and $B$ have decay constants $25 \lambda$ and $16 \lambda$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $B$ to that of $A$ will be "$e$" after a time $\frac{1}{a \lambda}$. The value of $a$ is $......$

Which of the following statements are true regarding radioactivity

$(I)$ All radioactive elements decay exponentially with time

$(II)$ Half life time of a radioactive element is time required for one half of the radioactive atoms to disintegrate

$(III)$ Age of earth can be determined with the help of radioactive dating

$(IV)$ Half life time of a radioactive element is $50\%$ of its average life periodSelect correct answer using the codes given belowCodes :

The half life of a radioactive isotope $X$ is $50$ years. It decays to another element $Y$ which is stable. The two elements $X$ and $Y$ were found to be in the ratio of $1 : 15$ in a sample of a given rock. The age of the rock was estimated to be..........$years$

The half life period of a radioactive substance is $5\, min$. The amount of substance decayed in $20\, min$ will be..........$\%$

The half-life of a radioactive element $A$ is the same as the mean-life of another radioactive element $B.$ Initially both substances have the same number of atoms, then